Node-Structured Integrative Gaussian Graphical Model Guided by Pathway Information

Abstract

Up to date, many biological pathways related to cancer have been extensively applied thanks to outputs of burgeoning biomedical research. This leads to a new technical challenge of exploring and validating biological pathways that can characterize transcriptomic mechanisms across different disease subtypes. In pursuit of accommodating multiple studies, the joint Gaussian graphical model was previously proposed to incorporate nonzero edge effects. However, this model is inevitably dependent on post hoc analysis in order to confirm biological significance. To circumvent this drawback, we attempt not only to combine transcriptomic data but also to embed pathway information, well-ascertained biological evidence as such, into the model. To this end, we propose a novel statistical framework for fitting joint Gaussian graphical model simultaneously with informative pathways consistently expressed across multiple studies. In theory, structured nodes can be prespecified with multiple genes. The optimization rule employs the structured input-output lasso model, in order to estimate a sparse precision matrix constructed by simultaneous effects of multiple studies and structured nodes. With an application to breast cancer data sets, we found that the proposed model is superior in efficiently capturing structures of biological evidence (e.g., pathways). An R software package nsiGGM is publicly available at author's webpage.

Microbiome Multi-Omics Network Analysis: Statistical Considerations, Limitations, and Opportunities

“…One typical application of Gaussian graphical models to multi-omics data is the joint Gaussian graphical model, which simultaneously estimates multiple graphical models under some constraints among them. The constraints are often determined by some prior knowledge for the multiple inverse covariance matrices such as their similarity in magnitudes or sparsity or the membership of nodes in biological pathways (Guo et al, 2011; Danaher et al, 2014; Kim et al, 2017). This idea has been applied to find biological networks from different groups simultaneously, e.g., disease subtypes or experimental conditions.…”

“…This idea has been applied to find biological networks from different groups simultaneously, e.g., disease subtypes or experimental conditions. For example, Kim et al (2017) used a joint Gaussian graphical model to estimate multiple mRNA expression networks from different datasets. Zhang et al (2016) further extended the idea of joint graphical models to a two-dimensional joint graphical lasso model.…”

Transcriptional Networks of Microglia in Alzheimer’s Disease and Insights into Pathogenesis

“…GGMs employ partial correlations, which measure the extent of linearity between two genes’ expression profiles in the context when the variability attributed to a third gene(s) expression profile is removed [54]. Briefly, GGMs are constructed by estimation of the inverse covariance matrix [55], which describes the “conditional dependence” between every two gene expression profiles. This enables the identification of direct gene–gene relationships or “conditional independence networks”, which have been found to reflect better biological network structures compared to “relevance networks” [56].…”